In the past, typical gutter covers have been formed with a substantially imperforate upper surface or top portion and with a relatively deep, water-channeling trough located near the area where the gutter cover is attached to the front lip of the gutter. This arrangement was believed to provide the most durability, leaf-shedding ability and pleasing appearance. However, the imperforate top, deep trough gutter cover was somewhat limited in its versatility. Likewise, the water-channeling trough tended to require a relatively elevated front wall that, in turn, occasionally resulted in difficulty mounting the rear portion of the gutter cover on the roof structure without changing the position of the gutter. As a result of these limitations, installing these conventional gutter covers could be relatively laborious or even impossible in the case of older structures such as half-round or box-style gutters.